Problem: Simplify the expression. $(-5y^{4}-y^{2}-2y)(-3y^{4}+6y^{2})$
Answer: First use the distributive property. $ - 5 y^4 (-3 y^4) - 5 y^4 (6 y^2) - y^2 (-3 y^4) - y^2 (6 y^2) - 2 y (-3 y^4) - 2 y (6 y^2) $ Simplify. $ 15y^{8} - 30y^{6} + 3y^{6} - 6y^{4} + 6y^{5} - 12y^{3} $ $15y^{8}-27y^{6}+6y^{5}-6y^{4}-12y^{3}$ Identify like terms. $ { 15y^{8}} {- 30y^{6}} {+ 3y^{6}} {- 6y^{4}} {+ 6y^{5}} {- 12y^{3}} $ Add the coefficients. $ { 15y^{8}} { -27y^{6}} {+ 6y^{5}} { -6y^{4}} { -12y^{3}} $